MN-MO 2007 Problem 1

Let $M$ be the midpoint of the side $BC$ of triangle $ABC$ . The bisector of the exterior angle of point $A$ intersects the side $BC$ in $D$ . Let the circumcircle of triangle $ADM$ intersect the lines $AB$ and $AC$ in $E$ and $F$ respectively. If the midpoint of $EF$ is $N$ , prove that $MN\parallel AD$ .